Of course for fun you can shoot recreational trap ( or skeet, sporting clays or five stand) with a side by side, or a pump, or even a Cooey for singles for that matter. If you get serious about competing and want to be competitive with your fellow shooters you will move to a more appropriate gun but for fun purposes shoot what you like! Don't pay attention to the gun snobs, they drive people away. As previously mentioned, the list of suitable side by sides in your price range is extremely small, mainly because few meet your price point. At $1500 or less all in you can't do better than a well cared for Browning BSS or Ithaca/SKB. Both are very robust guns, very well made from excellent material using sound designs and if not abused will hold their value indefinitely, may even appreciate slightly. There are a few Italian guns around, mostly unkown makers ( to us), most of them are fine, look in particular for Beretta and Bernardelli. Most German guns are very good, look for Merkel, Sauer, Geco, Simson for reliable makers. There are some good Belgian guns but few brand names to look for. There are loads of used Spanish doubles available , some good and some not. The problem is separating the good from the bad. In general look for an actual maker's name, not a catchy sales pitch such as " The Pheasant" or an importer's name like "International Imports". Companies like AYA, Sarasqueta and Union Armera made thousands of guns of all qualities but even their least expensive were good reliable guns. Used American doubles are frequently shot to death and the nicest ones are collectible and overpriced but if you can find a good one at a good price it may work for you. Be aware that many of these were stocked with excessive drop and kick like a mule. There are lots of fine British doubles around but most are over 100 years old, chambered for the short 2 1/2" shell and may be proofed for black powder cartridges only. They are beautiful guns but somewhat of a specialty field. Be aware that there are generally no parts available for any of these out of production guns, if it breaks repairs will be a problem.
New guns... not much choice in your price range other than CZ/Huglu. Most reports on these are generally favourable, not the quality of other guns that cost 3 or 4 or 10 times as much, but good value for the money. I'm quite sure that they would be perfectly suited to shooting hundreds of rounds a year but like all the others mentioned, they aren't designed or built to go 3,000, 5,000, 10,000 rounds a year like dedicated competitors do. That's why there is a solid steady demand for Perazzi, Kreighoff, Beretta and other target guns costing as much as a good late model used car.